As quantitative data become available for a particular form or function in the nervous system, it is advisable to attempt to assimilate the information into a comprehensive model of the underlying mechanisms and their interactions. This project consists in the development of such models, as well as the necessary analytical and mathematical techniques for their implementation and testing in several areas of experimental investigation carried out by LNLC members and in other laboratories. Analytical dendrite algorithms: Our initial 16-parameter algorithm for modeling motoneuron dendrites is a Monte Carlo method; it produces a finite ensemble of random trees. We now have several methods for directly calculating the statistical properties of all possible dendrites using the parameters of the distributions of particular dendrite attributes. The simplest form is an analytical expression with 3 parameters for the distribution of branch diameter of reach order. A more complete model with 6 parameters allows further calculation of the distributions of dendrite area and volume. Using the parameters of the full model we can calculate the expected number of branches of each diameter at each distance and the probabilities of a configuration of numbers of branches having each diameter, for computing the expected value of more complex attributes. Models of diffusion along axons: We have modeled passive diffusion along axons of dye injected into a ventral root of the chick embryo as it diffuses from the injection site to motoneurons in order to compare its time course with that of active transport, Dr. O'Donovan's measurements in this system agree in time course with the diffusion hypothesis.